TitleStructure of entropy solutions for multi-dimensional scalar conservation laws.
Publication TypeJournal Article
Year of Publication2003
AuthorsDe Lellis C., Otto F., Westdickenberg M.
JournalArchiv for Rational Mechanics and Analysis
Volume170
Pagination137–184
PublisherSpringer
Type of Articlescalar
ISSN0003-9527
KeywordsBV functions, entropy-entropy flux pair, finite entropy dissipation, geometric classification of blow-ups, shock wave
Abstract

An entropy solution u of a multi-dimensional scalar conservation law is not necessarily in BV, even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV function in the sense that the shock location is codimension-one rectifiable. This result highlights the regularizing effect of genuine nonlinearity in a qualitative way; it is based on the locally finite rate of entropy dissipation. The proof relies on the geometric classification of blow-ups in the framework of the kinetic formulation.

Notes

Arch. Ration. Mech. Anal. 170 (2003), no. 2, 137–184

URLhttp://www.springerlink.com/content/572jhd0jllt9wyre/
DOI10.1007/s00205-003-0270-9
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